Solving the equation

Answer:

c, b, a

Step-by-step explanation:

Because angles in a triangle add up to 180 degrees, we know that the unknown angle is 180-(55+68), or 57 degrees. Because of the side-angle inequality theorem, we know that B is equal to 57 degrees, C is equal to 68 degrees, and A is equal to 55 degrees.

68>57>55

c>b>a  

Answer:

D

Step-by-step explanation:

The option fourth represents the difference quotient of the function f(x) option fourth is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

[tex]\rm f(x) = - \sqrt{8x-35}[/tex]

[tex]\rm f(x+h) = - \sqrt{8(x+h)-35}\\\\\rm f(x+h) = - \sqrt{8x+8h-35}\\\\[/tex]

Difference quotient:

[tex]\rm = \dfrac{f(x+h)-f(x)}{h}[/tex]

[tex]\rm = \dfrac{- \sqrt{8x+8h-35}+ \sqrt{8x-35}}{h}[/tex]

After rationalization;

[tex]\rm = \dfrac{- \sqrt{8x+8h-35}+ \sqrt{8x-35}}{h} \times \dfrac{ \sqrt{8x+8h-35}+ \sqrt{8x-35}}{\sqrt{8x+8h-35}+ \sqrt{8x-35}}[/tex]

[tex]\rm = \dfrac{8}{-\sqrt{8x+8h-35}- \sqrt{8x-35} }[/tex]     , h ≠ 0

Thus, the option fourth represents the difference quotient of the function f(x) option fourth is correct.

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The class width used for the frequency distribution is 6.

The class midpoint for the class 23-29 is 26.

The class midpoint for the class 30-36 is 33.

The class midpoint for the class 37-43 is 40.

To find the class width of the frequency distribution, we need to determine the range of each age class. The range is the difference between the upper and lower boundaries of each class. Looking at the table, we can see that the class boundaries are as follows:

23-29

30-36

37-43

For the class 23-29, the lower boundary is 23 and the upper boundary is 29. To find the class width, we subtract the lower boundary from the upper boundary:

Class width = 29 - 23 = 6

So, the class width for the frequency distribution is 6.

To find the class midpoint for each class, we take the average of the lower and upper boundaries of each class.

For the class 23-29:

Class midpoint = (23 + 29) / 2 = 52 / 2 = 26

For the class 30-36:

Class midpoint = (30 + 36) / 2 = 66 / 2 = 33

For the class 37-43:

Class midpoint = (37 + 43) / 2 = 80 / 2 = 40

So, the class midpoint for the class 23-29 is 26, for the class 30-36 is 33, and for the class 37-43 is 40.

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Answer:

[tex]\frac{5}{11}[/tex]

Step-by-step explanation:

The line over 45 indicates 45 is being repeated, that is

0.4545....

Create 2 equations with the repeating values after the decimal point

let x = 0.4545..... → (1) ( multiply both sides by 100 )

100x = 45.4545..... → (2)

Subtract (1) from (2) eliminating the repeating decimal

99x = 45 ( divide both sides by 99 )

x = [tex]\frac{45}{99}[/tex] = [tex]\frac{5}{11}[/tex]

Thus 0.4545... = [tex]\frac{5}{11}[/tex]

Answer:

The answer is “B” (Reflects over the x-axis)

Step-by-step explanation:

Answer:

b.

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

3x + 2 = 11

subtract 2 from both sides

3x = 9

divide 3 on both sides

x = 3

Answer:

x=3

Step-by-step explanation:

3x + 2 = 11

subtract 2 from both sides

3x = 9

divide by 3

x=3--answer

Answer:

12 is the difference

Step-by-step explanation:

it has a range of 12˚ F

Answer:

12°F

Step-by-step explanation:

Use highest temp. - lowest temp. = difference.

Substitute in values: 3 - (-9) = 3 + 9

                                              = 12

Answer:

8 hours, and 25 mins

Step-by-step explanation:

7:30 am to 11:55am= 4 hours, 25 mins

1:00pm to 4:50 pm= 3 hours, 50 mins

Add together

Answer: 8 hours, and 25 mins.

Answer:

Step-by-step explanation:

n^3 + 512

512 = 8^3

So the factors are

(n + 8)(n^2 - nx + 64)

Answer:

try D(n+8) (n^2'8n+64)

Answer: 2

Step-by-step explanation:

96 = 4(5)(4) + 2(4)H

96 = 80 + 8H

96 - 80 = 8H

16 = 8H

16/8 = H

2 = H

Done!

Answer:

24000

Step-by-step explanation:

Step-by-step explanation:

i hope i have been useful buddy.

good luck ♥️♥️♥️♥️♥️.

Answer:

40 girls

Step-by-step explanation:

50/5=10

10*4=40

40 girls

Step-by-step explanation:

2x² + 5x − 6 = 0

The discriminant is:

D = b² − 4ac

D = 5² − 4(2)(-6)

D = 73

The discriminant is positive, so there are two real distinct roots.

Solving with quadratic formula:

x = [ -b ± √(b² − 4ac) ] / 2a

x = (-5 ± √73) / 4

Answer:

Step-by-step explanation:

f(1/2)=x2

f(1/2)=1/2^2

f(1/2)=1/4

Answer:

a) player’s expected payoff is $ 240

b) probability the player loses $1000 or more is 0.1788

c)  probability the player wins is 0.3557

d) probability of going broke is 0.0594

Step-by-step explanation:

Given:

Since there are 60 hands per hour and the player plays for four hours then the sample size is:

n = 60 * 4 = 240

The player’s strategy provides a probability of .49 of winning on any one hand so the probability of success is:

p = 0.49

a)

Solution:

Expected payoff is basically the expected mean

Since the bet is $50 so $50 is gained when the player wins a hand and $50 is lost when the player loses a hand. So

Expected loss =  μ

                        = ∑ x P(x)

                        = 50 * P(win) - 50 * P(lose)

                        = 50 * P(win) + (-50) * (1 - P(win))

                         = 50 * 0.49 - 50 * (1 - 0.49)

                        = 24.5 - 50 ( 0.51 )

                        = 24.5 - 25.5

                        = -1

Since n=240 and expected loss is $1 per hand then the expected loss in four hours is:

240 * 1 = $ 240

b)

Using normal approximation of binomial distribution:

n = 240

p = 0.49

q = 1 - p = 1 - 0.49 = 0.51

np = 240 * 0.49 = 117.6

nq = 240 * 0.51 = 122.5

both np and nq are greater than 5 so the binomial distribution can be approximated by normal distribution

Compute z-score:

z = x - np / √(np(1-p))

  = 110.5 - 117.6 / √117.6(1-0.49)

  = −7.1/√117.6(0.51)

  = −7.1/√59.976

  = −7.1/7.744417

  =−0.916789

Here the player loses 1000 or more when he loses at least 130 of 240 hands so the wins is 240-130 = 110

Using normal probability table:

P(X≤110) = P(X<110.5)

             = P(Z<-0.916)

             = 0.1788

c)

Using normal approximation of binomial distribution:

n = 240

p = 0.49

q = 1 - p = 1 - 0.49 = 0.51

np = 240 * 0.49 = 117.6

nq = 240 * 0.51 = 122.5

both np and nq are greater than 5 so the binomial distribution can be approximated by normal distribution

Compute z-score:

z = x - np / √(np(1-p))

  = 120.5 - 117.6 / √117.6(1-0.49)

  = 2.9/√117.6(0.51)

  = 2.9/√59.976

  = 2.9/7.744417

  =0.374463

Here the player wins when he wins at least 120 of 240 hands

Using normal probability table:

P(X>120) = P(X>120.5)

              = P(Z>0.3744)  

             =  1 - P(Z<0.3744)

             = 1 - 0.6443

             = 0.3557

d)

Player goes broke when he loses $1500

Using normal approximation of binomial distribution:

n = 240

p = 0.49

q = 1 - p = 1 - 0.49 = 0.51

np = 240 * 0.49 = 117.6

nq = 240 * 0.51 = 122.5

both np and nq are greater than 5 so the binomial distribution can be approximated by normal distribution

Compute z-score:

z = x - np / √(np(1-p))

  = 105.5 - 117.6 / √117.6(1-0.49)

  = -12.1/√117.6(0.51)

  = -12.1/√59.976

  = -12.1/7.744417

  =−1.562416

Here the player loses 1500 or more when he loses at least 135 of 240 hands so the wins is 240-135 = 105

Using normal probability table:

P(X≤105) = P(X<105.5)

             = P(Z<-1.562)

             = 0.0594

The Player’s expected payoff is $ 240.

Probability the player loses $1000 or more is 0.1788.

Probability the player wins is 0.3557.

Probability of going broke is 0.0594.

Given that,

There are 60 hands per hour and the player plays for four hours then the sample size is:

n = 60 × 4 = 240

The player’s strategy provides a probability of .49 of winning on any one hand so the probability of success is:

p = 0.49

Since the bet is $50 so $50 is gained when the player wins a hand and $50 is lost when the player loses a hand. So

Expected loss =  μ  = ∑ x P(x)

                        = 50 × P(win) - 50 P(loss)

                       = 50 × P(win) + (-50) × (1 - P(win)

                       = 50 × 0.49 - 50 × (1 - 0.49)

                      = 24.5 - 50 ( 0.51 )

                      = 24.5 - 25.5

                      = -1

Since n=240 and expected loss is $1 per hand then the expected loss in four hours is:

240 × 1 = $ 240

n = 240

p = 0.49

q = 1 - p = 1 - 0.49 = 0.51

np = 240 * 0.49 = 117.6

nq = 240 * 0.51 = 122.5

Both np and nq are greater than 5 so the binomial distribution can be approximated by normal distribution.

To Compute z-score:

[tex]z = \frac{x - np}{\sqrt{no (1-p )} } \\\\z = \frac{110.5 - 117.6}{\sqrt{117.6 ( 1-0.49)} }\\\\z = \frac{- 7.1}{\sqrt{117.6 (0.51) } } \\\\z = \frac{-7.1}{\sqrt{59.97} } \\\\z = \frac{-7.1}{7.74}\\\\z = - 0.916[/tex]

Here the player loses 1000 or more when he loses at least 130 of 240 hands so the wins is 240-130 = 110.

Using normal probability table:

P(X≤110) = P(X<110.5)

             = P(Z<-0.916)  = 0.1788

To compute z-score:

[tex]z = \frac{x - np}{\sqrt{no (1-p )} } \\\\z = \frac{120.5 - 117.6}{\sqrt{117.6 ( 1-0.49)} }\\\\z = \frac{2.9}{\sqrt{117.6 (0.51) } } \\\\z = \frac{2.9}{\sqrt{59.97} } \\\\z = \frac{2.9}{7.74}\\\\z = 0.34[/tex]

Here the player wins when he wins at least 120 of 240 hands.

By using normal probability table:

P(X>120) = P(X>120.5)

               =  1 - P(Z<0.3744)

               = 1 - 0.6443

              = 0.37

Both np and nq are greater than 5 so the binomial distribution can be approximated by normal distribution.

To Compute z-score:

[tex]z = \frac{x - np}{\sqrt{no (1-p )} } \\\\z = \frac{105.5 - 117.6}{\sqrt{117.6 ( 1-0.49)} }\\\\z = \frac{-12.1}{\sqrt{117.6 (0.51) } } \\\\z = \frac{-12.1}{\sqrt{59.97} } \\\\z = \frac{-12.1}{7.74}\\\\z = -1.56[/tex]

Here the player loses 1500 or more when he loses at least 135 of 240 hands so the wins is 240-135 = 105

Using normal probability table:

P(X≤105) = P(X<105.5)

               = P(Z<-1.562)

              = 0.54

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Answer:

17/20

0.8

75%

Step-by-step explanation:

17/20 is equal to 85%

0.8 is 80%

75%

Answer:

17/20, 0.8, 75%

Step-by-step explanation:

17 ÷ 20 = 0.85 or 85%

0.8 = 80%

From greatest to least, 17/20 → 0.8 → 75%.

Hope that helps.

Answer:

the answer is 37/7

Step-by-step explanation:

u multiply the 5 and the seven and add the 2 and u get 37/7 so u keep the denominator the same

Answer:

401

Step-by-step explanation:

Answer:

B. 55°

Step-by-step explanation:

they are alternate interior angles which mean they are congruent

The Volume formed by rotating the region enclosed by x = 10y and y^3 = x about the y-axis is 80π√10 cubic units.

To find the volume formed by rotating the region enclosed by the curves x = 10y and y^3 = x about the y-axis, we can use the method of cylindrical shells.

First, let's find the points of intersection between the two curves by setting them equal to each other:

10y = y^3

Rearranging the equation, we have:

y^3 - 10y = 0

Factoring out y, we get:

y(y^2 - 10) = 0

So, y = 0 or y^2 - 10 = 0

From y^2 - 10 = 0, we find two solutions: y = √10 and y = -√10. Since y≥0, we only consider y = √10.

Now, let's find the limits of integration. Since we are rotating about the y-axis, the limits of integration will be from y = 0 to y = √10.

To set up the integral for the volume, we consider an infinitesimally thin cylindrical shell with radius y, height Δy, and thickness Δx. The volume of each shell is given by:

dV = 2πxy Δx

We need to express x in terms of y using the given curves. From x = 10y, we have x = 10√y.

Substituting the values into the integral, we have:

V = ∫(0 to √10) 2π(10√y)(y) dy

V = 20π ∫(0 to √10) y^(3/2) dy

Using the power rule for integration, we can evaluate the integral:

V = 20π * (2/5) * y^(5/2) |(0 to √10)

V = 8π * (√10)^(5/2) - 8π * (0)^(5/2)

V = 8π * (√10)^5

Simplifying further:

V = 8π * 10√10

V = 80π√10

Therefore, the volume formed by rotating the region enclosed by x = 10y and y^3 = x about the y-axis is 80π√10 cubic units.

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Answer:

sksjjsksjsksjsjzjjzjjzhzhhzjzj

it can't be simplified more